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Derivative of $$$- \frac{\sin{\left(t \right)}}{2}$$$

The calculator will find the derivative of $$$- \frac{\sin{\left(t \right)}}{2}$$$, with steps shown.

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Find $$$\frac{d}{dt} \left(- \frac{\sin{\left(t \right)}}{2}\right)$$$.

Solution

Apply the constant multiple rule $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$ with $$$c = - \frac{1}{2}$$$ and $$$f{\left(t \right)} = \sin{\left(t \right)}$$$:

$${\color{red}\left(\frac{d}{dt} \left(- \frac{\sin{\left(t \right)}}{2}\right)\right)} = {\color{red}\left(- \frac{\frac{d}{dt} \left(\sin{\left(t \right)}\right)}{2}\right)}$$

The derivative of the sine is $$$\frac{d}{dt} \left(\sin{\left(t \right)}\right) = \cos{\left(t \right)}$$$:

$$- \frac{{\color{red}\left(\frac{d}{dt} \left(\sin{\left(t \right)}\right)\right)}}{2} = - \frac{{\color{red}\left(\cos{\left(t \right)}\right)}}{2}$$

Thus, $$$\frac{d}{dt} \left(- \frac{\sin{\left(t \right)}}{2}\right) = - \frac{\cos{\left(t \right)}}{2}$$$.

Answer

$$$\frac{d}{dt} \left(- \frac{\sin{\left(t \right)}}{2}\right) = - \frac{\cos{\left(t \right)}}{2}$$$A

Related Notes: Definition of Derivative , Derivatives of Elementary Functions , Table of Derivatives , Related Rates , Studying Derivative Graphically , Optimization Problems , Applications to Economics , Constant Multiple Rule , Sum and Difference Rules , Product Rule , Quotient Rule , Chain Rule , Derivative of Inverse Function